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Machine learned potentials (MLPs) have been widely employed in molecular dynamics simulations to study thermal transport. However, the literature results indicate that MLPs generally underestimate the lattice thermal conductivity (LTC) of typical solids. Here, we quantitatively analyze this underestimation in the context of the neuroevolution potential (NEP), which is a representative MLP that balances efficiency and accuracy. Taking crystalline silicon, gallium arsenide, graphene, and lead telluride as examples, we reveal that the fitting errors in the machine-learned forces against the reference ones are responsible for the underestimated LTC as they constitute external perturbations to the interatomic forces. Since the force errors of a NEP model and the random forces in the Langevin thermostat both follow a Gaussian distribution, we propose an approach to correcting the LTC by intentionally introducing different levels of force noises via the Langevin thermostat and then extrapolating to the limit of zero force error. Excellent agreement with experiments is obtained by using this correction for all the prototypical materials over a wide range of temperatures. Based on spectral analyses, we find that the LTC underestimation mainly arises from increased phonon scatterings in the low-frequency region caused by the random force errors. [ABSTRACT FROM AUTHOR]

The spectrum of localized hole states (traps) in amorphous silicon nitride, a-Si3N4, is experimentally studied using the method of thermally stimulated depolarization. The experiment is compared with theoretical calculations using three models of the energy spectrum of traps: discrete spectrum (monoenergetic trap), continuous spectrum, and Gaussian trap distribution. The experiment is quantitatively described by a model of a discrete spectrum of traps with an energy of 1.15 eV and a width of no more than 0.01 eV. In the case of a continuous and Gaussian spectrum of traps, the contribution to depolarization is made by the deepest traps. The blurring of the trap energy level in a-Si3N4 due to the absence of long-range order (fluctuations in the Si–N bond length and fluctuations in the N–Si–N and Si–N–Si angles) does not exceed 0.01 eV. [ABSTRACT FROM AUTHOR]

Magnetic and magnetocaloric properties of L a 0.85 S r 0.15 M n 0.99 F e 0.01 O 3 perovskite oxides are investigated in the framework of the mean-field theory with a goal to develop a comprehensive model with parameters that can be used to optimize the caloric performances for cooling applications. Using the experimental magnetic isotherms M(H,T), we estimate and compare the exchange parameter (λ) , the saturation magnetization (M 0) , the total angular momentum (J) , and the gyromagnetic factor (g) for two different samples annealed at 1170 and 1250 °C. These parameters are used, in turn, in the simulation of the magnetic and the magnetocaloric properties of these L a 0.85 S r 0.15 M n 0.99 F e 0.01 O 3 compounds assuming imperfect samples with compositional and/or magnetic inhomogeneities. For this purpose, a Gaussian distribution of the Curie temperature is assumed. The temperature dependence of the magnetic entropy change, − Δ S M (T) , resulting from an applied field variation is simulated for both samples. The selected distribution captures the rounding of the − Δ S M (T) peak at its maximum and its broadening with growth conditions, features that are constantly observed in many bulk polycrystalline compounds. [ABSTRACT FROM AUTHOR]

We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer–counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards–Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil–globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories. [ABSTRACT FROM AUTHOR]

Planning decisions are generally subject to some level of uncertainty. In forestry, data describing the resources available have a major impact on operations performance and productivity. This paper aims to present a method to improve decision-making in the forest supply chain by taking supply uncertainty into account using the results of data quality assessments. The case study describes the operations planning process of a Canadian forest products company dealing with an uncertain volume of wood supply. Three approaches to constructing probability distributions based on data quality are tested. Each approach offers a different level of precision: (1) a frequency distribution of accuracy, (2) a normal distribution based on average accuracy, and (3) a normal distribution based on data quality classification. Using stochastic programming to plan transport and production shows that lower costs can be achieved with a general characterisation of the data accuracy. Not considering uncertainty when planning operations leads to a significant replanning transportation cost. Using classes of data quality to include uncertainty in operations planning contributes to reducing the transportation cost from $15.90/m3 down to $15.32/m3 representing 3.6%. [ABSTRACT FROM AUTHOR]

The role of curvature effects, in the thermal-field (TF) emission of electrons from nanotips, has been investigated. It is found that for field emitter tips having tip radius of curvature R a < 50 nm, the error on using the planar tunneling potential to evaluate the current density is significant compared to the curvature-corrected potential. Furthermore, the error is found to be strongly temperature dependent at low apex fields, whereas at high fields, it is only moderate. For emitter tips having tip radius R a ≥ 5 nm, a unified expression for current density applicable for field, thermal-field, and thermionic emission is obtained. In the analysis, a single linearization point corresponding to the peak of the normal energy distribution of electrons is chosen, about which the Gamow exponent is expanded. The temperature-dependent curvature-corrected current density equation is numerically validated against a benchmark that performs the current density integral with the Kemble form of the Wentzel–Kramers–Brillouin transmission coefficient up to the peak of the tunneling potential, while above the barrier, the Morse transmission coefficient is used. The agreement is found to be good. It is inferred that the curvature plays a significant role in field and thermal-field emission, whereas in thermionic emission, it is not as important. In the limit where the apex radius of curvature R a → ∞ , it is able to retrieve the Murphy–Good equation as well as the Richardson–Laue–Dushman equation in their respective limits. [ABSTRACT FROM AUTHOR]

Platform-based product development is a cost-efficient approach to satisfy wide range of customer preferences. One important problem is the product platform configuration, in which two types of platform configuration are widely used, either module selection or module integration. The platform configuration based on module selection provides a broader solution space of platform selection, while module integration facilitates product platform commonality to gain economic benefits. Up to date, most research focused on the platform configuration based on module selection with a given module set. In this paper, we propose a new model to determine the optimal platform configuration for an external product family, considering both module selection and integration. The demand for the external product family is uncertain and assumed to follow normal distribution. A hybrid methodology combining simulated annealing and variable neighbourhood search is proposed. A numerical examination is carried out for the purpose of evaluation. The results show that the proposed model can provide a practically good solution. Main contributions of this research are two folds, one is the balance point between module selection and module integration in the platform configuration and the other is that we take into account the operation cost of module acquisition to the platform configuration problem. [ABSTRACT FROM AUTHOR]

A random variable X has a standard normal distribution if and only if E [ f ′ (X) ] = E [ X f (X) ] for any continuous and piecewise continuously differentiable function f such that the expectations exist. This first-order characterizing equation, called the Stein identity, has been extended to other univariate distributions. For the multivariate normal distribution, a number of Stein identities have already been developed, all of them second order equations. In this study, we developed a new Stein characterization for the bivariate normal distribution. Unlike many existing multivariate versions in the literature, ours is a system of first-order equations which has the univariate Stein identity as a special case. We also constructed a generalized Stein characterization for other absolutely continuous bivariate distributions. Finally, we illustrated how this Stein characterization looks like for some known absolutely continuous bivariate distributions. [ABSTRACT FROM AUTHOR]

This study investigates the impact of Al 2 O 3 particle volume fraction and distribution on the deformation and damage of particle-reinforced metal matrix composites, particularly in the context of functionally graded metal matrix composites. In this study, a two-dimensional nonlinear random microstructure-based finite element modeling approach implemented in ABAQUS/Explicit with a Python-generated script to analyze the deformation and damage mechanisms in AA 6061 - T 6 / Al 2 O 3 composites. The plastic deformation and ductile cracking of the matrix are captured using the Gurson–Tvergaard–Needleman model, whereas particle fracture is modelled using the Johnson–Holmquist II model. Matrix-particle interface decohesion is simulated using the surface-based cohesive zone method. The findings reveal that functionally graded metal matrix composites exhibit higher hardness values (HRB ) than traditional metal matrix composites. The results highlight the importance of functionally graded metal matrix composites. Functionally graded metal matrix composites with a Gaussian distribution and a particle volume fraction of 10% achieve HRB values comparable to particle-reinforced metal matrix composites with a particle volume fraction of 20%, with only a 2% difference in HRB . Thus, HRB can be improved significantly by employing a low particle volume fraction and incorporating a Gaussian distribution across the material thickness. Furthermore, functionally graded metal matrix composites with a Gaussian distribution exhibit higher HRB values and better agreement with experimental distribution functions when compared to those with a power-law distribution. [ABSTRACT FROM AUTHOR]

Background Purpose Methods Results Conclusions The diffusion and perfusion parameters derived from intravoxel incoherent motion (IVIM) imaging provide promising biomarkers for noninvasively quantifying and managing various diseases. Nevertheless, due to the distribution gap between simulated and real datasets, the out‐of‐distribution (OOD) problem occurred in supervised learning‐based methods degrades their performance and hinders their real applications.To address the OOD problem in supervised methods and to further improve the accuracy and stability of IVIM parameter estimation, this work proposes a novel learning framework called IterANN, based on mean deviation prior (MDP) between training and estimated IVIM parameters on the test set.Specifically, MDP indicates that the mean of the estimated IVIM parameters always locates between the mean of IVIM parameters in the test and train sets. In IterANN, we adopt a very simple artificial neural network (ANN) architecture of two hidden layers with 12 neurons per hidden layer, an input layer containing the signals acquired at multiple b‐values and an output layer composed of three IVIM parameters (D$D$, F$F$ and DStar$DStar$). Inspired by MDP, the distribution of IVIM parameters in the training set (simulated data) is iteratively updated so that their mean gradually approaches the predicted values of the real data. This aims to achieve a strong correlation between the simulated data and the real data. To validate the effectiveness of IterANN, we compare it with several methods on both simulation and real acquisition datasets, including 21 healthy and 3 tumor subjects, in terms of residual errors of IVIM parameters or DW signals, the coefficients of variation (CV) of IVIM parameters, and the parameter contrast‐to‐noise ratio (PCNR) between normal and tumor tissues.On two simulation datasets, the proposed IterANN achieves the lowest residual error in IVIM parameters, especially in the case of low signal‐to‐noise ratio (SNR = 10), the residual error of D$D$, F$F$ and DStar$DStar$ is decreased by 15.82%/14.92%,81.19%/74.04%,50.77%/1.549%$15.82\%/14.92\%, 81.19\%/74.04\%, 50.77\%/1.549\%$ (Gaussian distribution /realistic distribution) respectively comparing to the suboptimal method. On real dataset, the IterANN achieves the highest PCNR when comparing the normal and tumor regions. Additionally, the proposed IterANN demonstrated better stability, with its CV being significantly lower than that of other methods in the vast majority of cases (p<0.01$p<0.01$, paired‐sample Student's t‐test).The superior performance of IterANN demonstrates that updating the distribution of the train set based on MDP can effectively solve the OOD problem, which allows us not only to improve the accuracy and stability of the estimated IVIM parameters, but also to increase the potential of IVIM in disease diagnosis. [ABSTRACT FROM AUTHOR]

Key points Physiologists often express the change in the value of a measurement made on two occasions as a ratio of the initial value. This is usually motivated by an assumption that the absolute change fails to capture the true extent of the alteration that has occurred in attaining the final value – if there is initial variation among individual cases. While it may appear reasonable to use ratios to standardize the magnitude of change in this way, the perils of doing so have been widely documented. Ratios frequently have intractable statistical properties, both when taken in isolation and when analysed using techniques such as regression. A new method of computing a standardized metric of change, based on principal components analysis (PCA), is described. It exploits the collinearity within sets of initial, absolute change and final values. When these sets define variables subjected to PCA, the standardized measure of change is obtained as the product of the loading of absolute change onto the first principal component (PC1) and the eigenvalue of PC1. It is demonstrated that a sample drawn from a population of these standardized measures: approximates a normal distribution (unlike the corresponding ratios); lies within the same range; and preserves the rank order of the ratios. It is also shown that this method can be used to express the magnitude of a physiological response in an experimental condition relative to that obtained in a control condition. The intractable statistical properties of ratios and the perils of using ratios to standardize the magnitude of change are well known. A new method of computing a standardized metric, based on principal components analysis (PCA), is described, which exploits the collinearity within sets of initial, absolute change and final values. A sample drawn from a population of these PCA‐derived measures: approximates a normal distribution (unlike the corresponding ratios); lies within the same range as the ratios; and preserves the rank order of the ratios. The method can also be applied to express the magnitude of a physiological response in an experimental condition relative to a control condition. [ABSTRACT FROM AUTHOR]

Eddy current dampers (ECDs), which employ magnetic induction to produce eddy current damping for energy dissipation, demonstrate superior sensitivity and durability in comparison to traditional viscous dampers. However, the inherent, velocity-dependent nonlinearity of ECDs poses significant challenges in research and engineering implementations. The present study addresses this challenge by exploring the stochastic linearization of ECDs, innovatively incorporating the non-Gaussian distribution of velocity responses. Central to our analysis, we proposed four closed-form expressions for the equivalent damping ratios of ECDs, derived from both Gaussian and non-Gaussian distributions. This achievement is facilitated by the utilization of the statistical linearization technique (SLT), which integrates both force-based and energy-based equivalent criteria. To validate the accuracy of these expressions, Monte Carlo simulation (MCS) was employed. Our results demonstrate that, regardless of soil conditions and velocity distributions, the force-based criteria, in most cases, outperform the energy-based criteria in assessing the stochastic linearization of ECDs. Notably, in scenarios where ECD nonlinearity is prominent, the probability density of the exact velocity response of ECDs in firm soil exhibits a significantly steeper profile near zero, resembling an exponential-like distribution more closely than the Gaussian distribution. Conversely, in soft soil conditions, the actual velocity distribution lies intermediate between Gaussian and exponential-like distributions. Additionally, a series of parameter studies were conducted, further revealing that the force-based Gaussian SLT method offers the highest accuracy in soft soil and firm soil with critical velocities exceeding 0.05m/s. In contrast, the force-based non-Gaussian SLT method proves to be the more precise approach in firm soil with critical velocities below 0.05m/s. [ABSTRACT FROM AUTHOR]

We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function. [ABSTRACT FROM AUTHOR]

A large number of objects of different scales appear aggregative distribution in remote sensing images, which brings two challenges to remote sensing object detection. The first challenge arises from the presence of objects with large scale differences within the same scene, which complicates the detector's ability to balance the detection performance between large and small objects. The second challenge is that the distribution of dense objects on remote sensing images with complex backgrounds can reduce the feature representation capability of the network, leading to false detections and missed detections of objects. To address the two challenges present in remote sensing object detection, we propose a new object detection network DA-GLANet (Direction-Aware Multi-Branch Attention and Gaussian Label Assignment Balance Net). For the first challenge, we designed a multi-scale feature fusion module to fully utilize semantic information at different scales, thereby improving the detection accuracy of multi-scale objects. Subsequently, to tackle the second challenge, we proposed a multi-branch attention module with direction-aware capabilities. This module can enhance the network's feature representation of objects of interest by generating attention maps that are both direction-aware and position-sensitive. In addition, we propose a label assignment strategy based on Gaussian distribution to address the imbalance of positive and negative labels caused by the complexity of remote sensing images. These methods work synergistically to improve aggregative object detection accuracy. We have conducted extensive experiments on the DOTA dataset, Levir dataset, and WHU buildings change detection dataset to demonstrate the superiority of our method. On the DOTA dataset, our method improves mAP by 0.4%, 0.3%, and 0.2% compared to the top three methods. On the Levir dataset, our method improves mAP by 2.5%, 2.2%, and 1.6% compared to the top three methods. [ABSTRACT FROM AUTHOR]

A statistical study was made of the summer extreme temperatures over peninsular Spain in the last forty years. Records from 158 observatories regularly distributed over Iberia with no missing data were available for the common period from 1981 to 2020. For this purpose, a hierarchical spatio-temporal model with a Gaussian copula and a generalized extreme value parametrization of the extreme events was used. The temporal trend in maximum extreme temperatures was studied making use of both a stationary model and a nonstationary one that takes into account the influence of anthropogenic climate change on extreme temperatures using the global mean temperature as a function of time for the study period. The results led to a better fit of the nonstationary model, with there being a 3.5-fold greater increase in the 20-year return level of the extreme temperatures than in that corresponding to the global mean temperature. [ABSTRACT FROM AUTHOR]

Tightness remains the primary goal in all modern estimation bounds. For very weak signals, tightness is enabled by appropriately selecting the prior probability distribution and bound family. While current bounds in global navigation satellite systems (GNSSs) assess the performance of carrier frequency estimators under Gaussian or uniform assumptions, the circular nature of frequency is overlooked. Of all bounds in the Bayesian framework, the Weiss--Weinstein bound (WWB) stands out because it is free from regularity conditions or restrictions on the prior distribution. Therefore, the WWB is extended for the current frequency estimation problem. A divide-and-conquer type of hyperparameter tuning method is developed to mitigate issues of computational complexity for the WWB family while enhancing tightness. Synthetic results show that for a von Mises prior probability distribution, the WWB provides a bound up to 22.5% tighter than the Ziv--Zakaï bound when the signal-to-noise ratio varies between -3.5 dB and -20 dB, where the GNSS signal is deemed extremely weak. [ABSTRACT FROM AUTHOR]

In this research article, we introduced the notion of q-probabilty distributions in quantum calculus. We characterized the concept of q-density by connecting it to a probability measure and investigated some of their outstanding properties. In this case, the Transfer theorem was extended in order to compute afterwards the q-moments, q-entropy, q-moment generating function, and q-quantiles. We are also interested in finding the centered q-Gaussian distribution N q (0 , σ 2) with variance σ 2 . We also proved that this q-distribution belongs to a class of classical discrete distributions. The centered q-Gaussian law N q (0 , σ 2) is also naturally related to the q-Gaussian distribution N q (μ , σ 2) with mean μ and standard deviation σ. We corroborated that the q-moments of these q-distributions are q-analogs of the moments of classical distributions. Numerical studies demonstrated that N q (0 , σ 2) interpolates between the classical Uniform and Gaussian distributions when q goes to 0 and 1, respectively. Subsequently, simulation studies for various q parameter values and samples sizes of the Gaussian q-distributions were conducted to demonstrate the effectiveness of the proposed model. Eventually, we provided some pertinent closing remarks and offered new perspectives for future works. [ABSTRACT FROM AUTHOR]

In this paper, we propose a failure-informed multi-stage training algorithm for approximating the double-valley dark soliton solutions of the three-component nonlinear Schrödinger equation (NLSE). Although the physics-informed neural network (PINN) method has achieved remarkable results in many equations, it is ineffective when directly applied to the considered equation due to the non-vanishing background of dark solitons and the complexity of the multi-valley structure. To improve the approximation ability of the PINN, the algorithm we proposed generates effective samples adaptively based on Gaussian mixture distribution by combining the time-adaptive strategy, failure-informed enrichment technique, and pre-fixed technique. Furthermore, the algorithm is extended to learn the solution operator of three-component NLSE within a specialized solution space. The results of numerical simulation demonstrate that the improved algorithm has better approximation ability and faster convergence rate in approximating the solution and solution operator of the considered equation while using a smaller training set. • We explore a deep learning method for solving three-component nonlinear Schrödinger equation. • We proposed an improved PINNS by time-adaptive strategy, failure-informed enrichment technique, and pre-fixed technique. • The data-driven double-valley dark soliton solutions are derived by the proposed method. • The proposed method can be easily extended to the physics-informed DeepONets. [ABSTRACT FROM AUTHOR]

Event cameras, characterized by their low power consumption, expansive dynamic range, and high temporal resolution, have attracted great attentions in various computer vision tasks. Compared to frame-based cameras, event cameras exemplify a marked paradigmatic transition in data formation and output. However, the quality of event streams is compromised by background activity and hot pixels, leading to increased computational overheads and sub-optimal outcomes in subsequent applications, notably in recognition, video reconstruction, and target detection tasks. In this paper, a two-step denoising algorithm (referred as GMCM) is proposed to counteract these challenges. The GMCM algorithm comprises two steps: Gaussian denoising preprocessing and motion denoising. The former incorporates Gaussian temporal distribution and adaptive thresholding mechanisms to discern the inclusion of motion-related information within the event streams. Experimental results demonstrate that Gaussian denoising preprocessing can not only adeptly discern whether the event data stream contains motion information but also enhance computational efficiency. Conclusively, the GMCM algorithm achieves state-of-the-art performance, yielding SNR scores of 37.22 and 26.79 on the DVSCLEAN dataset at the noise ratios of 50% and 100%, respectively. [ABSTRACT FROM AUTHOR]

The main concern is the uncertainty in the real-world solid transportation problem. This study examines a supply, demand, and conveyance capacity-based multi-choice solid stochastic multi-objective transportation problem (MCSS-MOTP). Due to uncertainty, the concrete objective function coefficients of the proposed model are of multivariate type. Furthermore, the parameters of the constraints are treated as independent multivariate random variables with normal distribution. First, a Newton divided difference method-based interpolation polynomial is described that extends an interpolation polynomial using practical properties at non-negative integer nodes to deal with any multiple-choice parameter. Second, the probabilistic constraints are converted into precise ones utilizing a stochastic programming approach. In the end, ranking procedure was used to compare the existing approach with the old models. The proposed model’s applicability was confirmed using a numerical example. [ABSTRACT FROM AUTHOR]

A reduced‐rank mixed‐effects model is developed for robust modelling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the association of the two functional variables is modelled through the association of the principal component scores. A multivariate‐scale mixture of normal distributions is used to model the principal component scores and the measurement errors in order to handle outlying observations and achieve robust inference. The mean functions and principal component functions are modelled using splines, and roughness penalties are applied to avoid overfitting. An EM algorithm is developed for computation of model fitting and prediction. A simulation study shows that the proposed method outperforms an existing method, which is not designed for robust estimation. The effectiveness of the proposed method is illustrated through an application of fitting multiband light curves of Type Ia supernovae. [ABSTRACT FROM AUTHOR]

patterns is a requisite for the design and operation of water distribution networks. This study uses end-use water consumption data to create zonal water consumption patterns. The process involves extrapolating end-use data to create flow variation in the water distribution network. In this study, the water consumption patterns of 30 household consumers as the end-use data were monitored for a period of one year. To validate the results of the presented methodology, zonal water consumption patterns of nine district-metered areas were also measured. The Normal and the Gumbel probability distributions were applied to individual water consumption patterns to generate comprehensive zonal water consumption patterns for different population sizes. The results indicate that the maximum Gumbel's probabilistic distribution function with considering the leakage effect created better results. This innovative approach holds the potential to create comprehensive zonal water consumption patterns tailor-made for different population sizes. [ABSTRACT FROM AUTHOR]

Supplier selection and order allocation are important issues in supply chain management. Several features differentiate this research from other studies. The two-echelon supply chain network studied in this research comprises of suppliers and production centers. The supply chain model is a multi-site, multi-mode, and multi-item model which incorporates multiple sites for production centers, multiple transportation modes, and multiple purchased items from suppliers. In this model, demand, delivery delay, and percentage of defective items are deemed stochastic parameters. It is assumed that these uncertain parameters have normal distributions with known means and standard deviations. The most significant contribution of this research is incorporating uncertainty with two indicators of mean and standard deviation into a multi-objective model for the supplier selection and order allocation problem. To deal with stochastic demand, the chance constraint approach is applied. The multi-objective optimization model aims to minimize purchasing cost, delivery delay, and defective items. To solve this model, first, a mixed-integer formulation is established to address the order allocation problem. Then, after using the epsilon constraint method, the Torabi-Hassini approach is used to transform the multi-objective model into an equivalent single-objective model. Real data from poultry and dairy industries are used to evaluate the model performance. Sensitivity analysis shows that the most improvements in the objective functions occur when the means and standard deviations of delivery delay and percentage of defective items for suppliers and transportation modes are decreased simultaneously. [ABSTRACT FROM AUTHOR]

Hysteresis curves of commercial Alnico 5 and Alnico 2 magnets were evaluated with the anisotropic Stoner-Wohlfarth model. Alnico 2 is an isotropic magnet, whereas Alnico 5 is an anisotropic magnet. These magnets have five main alloying elements: Al, Fe, Ni, Co and Cu. The described method allows a direct estimate of the shape anisotropy in any commercial Alnico magnet, avoiding laborious production of single crystals. Besides, the magnetic anisotropy of any sample with fiber texture can be determined. Parameters related to magnetic shape anisotropy can be directly extracted from the hysteresis of either isotropic or anisotropic Alnico magnets. A shape anisotropy of 1.4 kOe was estimated for the isotropic Alnico 2. The shape anisotropy of the anisotropic Alnico 5 was estimated at 2.2 kOe. The magnetic texture of the Alnico 5 sample can be well described by a Gaussian distribution and remanence to saturation ratio, Mr/Ms, of 0.931. A spring effect is observed in the hysteresis of the Alnico 2 and Alnico 5 magnets, confirming that the ferromagnetic phase is single domain size and that the mechanism of reversal is coherent rotation. [ABSTRACT FROM AUTHOR]

L. Klebanov proved the following theorem. Let ξ 1 , ⋯ , ξ n be independent random variables. Consider linear forms L 1 = a 1 ξ 1 + ⋯ + a n ξ n , L 2 = b 1 ξ 1 + ⋯ + b n ξ n , L 3 = c 1 ξ 1 + ⋯ + c n ξ n , L 4 = d 1 ξ 1 + ⋯ + d n ξ n , where the coefficients a j , b j , c j , d j are real numbers. If the random vectors (L 1 , L 2) and (L 3 , L 4) are identically distributed, then all ξ i for which a i d j - b i c j ≠ 0 for all j = 1 , n ¯ are Gaussian random variables. The present article is devoted to an analog of the Klebanov theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers. [ABSTRACT FROM AUTHOR]

Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution and a suitable Gaussian process. Our explicit inequalities indicate how the hidden and output layers sizes affect the Gaussian behaviour of the network and quantitatively recover the distributional convergence results in the wide limit, i.e., if all the hidden layers sizes become large. [ABSTRACT FROM AUTHOR]

This paper deals with estimating the underlying parameter of a length-biased inverse Gaussian distribution, when the observations are prone to length-biased sampling. Length-biased sampling occurs when the observations of smaller lengths or dimensions are neglected from the sample. We focus on a particular type of sequential fixed-accuracy confidence interval for estimation purposes. This method proves to be both time and cost efficient as one is able to perform the estimation using an optimal number of observations according to some set criteria. We discuss the applicability of our proposed method with regards to estimating the cluster size of the "Eastern Tropical Pacific Dolphins", which are often vulnerable to length biasedness. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices. This method integrates features including photovoltaic (PV) systems, energy storage coupling, varied energy roles, and energy supply and demand dynamics. The system model is developed by considering energy devices as versatile units capable of fulfilling various functionalities and playing multiple roles simultaneously. To strike a balance between optimality and feasibility, renewable energy resources are modeled with considerations for forecasting errors, Gaussian distribution, and penalty factors. Furthermore, this study introduces a distributed event-triggered surplus algorithm designed to address the economic dispatch problem by minimizing production costs. Rooted in surplus theory and finite time projection, the algorithm effectively rectifies network imbalances caused by directed graphs and addresses local inequality constraints. The algorithm greatly reduces the communication burden through event triggering mechanism. Finally, both theoretical proofs and numerical simulations verify the convergence and event-triggered nature of the algorithm. [ABSTRACT FROM AUTHOR]

Background: Positron emission tomography (PET) traditionally uses coincident annihilation photons emitted from a positron interacting with an electron to localize cancer within the body. The formation of positronium (Ps), a bonded electron-positron pair, has not been utilized in clinical applications of PET due to the need to detect either the emission of a prompt gamma ray or the decay of higher-order coincident events. Assessment of the lifetime of the formed Ps, however, can potentially yield additional diagnostic information of the surrounding tissue because Ps properties vary due to void size and molecular composition. To assess the feasibility of measuring Ps lifetimes with a PET scanner, experiments were performed in a Biograph Vision Quadra (Siemens Healthineers). Quadra is a long-axial field-of-view (LA-FOV) PET scanner capable of producing list-mode data from single interaction events. Results: Ortho-Ps (o-Ps) lifetimes were measured for quartz-glass and polycarbonate samples using a 22 Na positron source. Results produced o-Ps lifetimes of 1.538 ± 0.036 ns for the quartz glass and 1.927 ± 0.042 ns for the polycarbonate. Both o-Ps lifetimes were determined using a double-exponential fit to the time-difference distribution between the emission of a prompt gamma ray and the annihilation of the correlated positron. The measured values match within a single standard deviation of previously published results. The quartz-glass samples were additional measured with 82 Rb , 68 Ga and 124 I to validate the lifetime using clinically available sources. A double-exponential fit was initially chosen as a similar methodology to previously published works, however, an exponentially-modified Gaussian distribution fit to each lifetime more-accurately models the data. A Bayesian method was used to estimate the variables of the fit and o-Ps lifetime results are reported using this methodology for the three clinical isotopes: 1.59 ± 0.03 ns for 82 Rb , 1.58 ± 0.07 ns for 68 Ga and 1.62 ± 0.01 ns for 124 I . The impact of scatter and attenuation on the o-Ps lifetime was also assessed by analyzing a water-filled uniform cylinder (20 ϕ × 30 cm 3 ) with an added 82 Rb solution. Lifetimes were extracted for various regions of the cylinder and while there is a shape difference in the lifetime due to scatter, the extracted o-Ps lifetime of the water, 1.815 ± 0.013 ns, agrees with previously published results. Conclusion: Overall, the methodology presented in this manuscript demonstrates the repeatability of Ps lifetime measurements with clinically available isotopes in a commercially-available LA-FOV PET scanner. This validation work lays the foundation for future in-vivo patient scans with Quadra. [ABSTRACT FROM AUTHOR]

In this paper, we take variable separation method to study Klein–Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy–Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel family of procedures for deriving a discrete counterpart to a continuous probability distribution. They are based on a class of distances between cumulative distribution functions, including the Cramér, the Cramér-von Mises, and the Anderson-Darling distances as particular cases. The discrete counterpart is defined and derived as the random variable which minimizes its distance to the assigned continuous probability distribution among all the discrete random variables supported on the set of integers (or positive integers). Applications are provided with reference to the exponential and the normal distributions, among others; the discrete counterparts are derived, and their main properties are discussed, also in comparison with the one obtained through an existing discretization technique based on the preservation of the cumulative distribution function at integer values. Parameter estimation for these discrete analogs is discussed, along with an analysis of two real datasets, where they are compared in terms of goodness-of-fit with some popular discrete distributions. Furthermore, in order to highlight the effectiveness and the benefits derived from the proposed discretization procedures, we illustrate two practical applications in actuarial science and in reliability engineering. In the former case, the problem of determining the distribution of the total claims amount for a non-life insurance portfolio is considered, where the claim sizes can be modelled as iid random variables, and the number of claims is random as well. Actuaries use a recursive calculation method based on Panjer's formula, which requires an appropriate discretization of the individual claim distribution, and therefore the proposed procedures can be used. Since we consider two simple cases where the distribution of the total claims amount is analytically acquirable, the efficacy of the discretization procedures in the final approximation can be easily assessed and turns out to be satisfactory, especially when compared to the existing discretization. The latter case considers the determination of the reliability parameter for a complex stress-strength model. Here, the approximation by discretization is compared to Monte Carlo simulation and shown to be relevant: with a comparable if not smaller computational effort, discretization leads to similar results as simulation. Such discretizations can also naturally be applied to more complex problems such as scenario generation in stochastic programming. R code for this article is provided as supplementary material. [ABSTRACT FROM AUTHOR]

Using ‘working’ assumptions on conditional third and fourth moments of errors, we propose a method of moments estimator that can have improved efficiency over the popular Gaussian quasi‐maximum likelihood estimator (GQMLE). Higher‐order moment assumptions are not needed for consistency – we only require the first two conditional moments to be correctly specified – but the optimal instruments are derived under these assumptions. The working assumptions allow both asymmetry in the distribution of the standardized errors as well as fourth moments that can be smaller or larger than that of the Gaussian distribution. The approach is related to the generalized estimation equations (GEE) approach – which seeks the improvement of estimators of the conditional mean parameters by making working assumptions on the conditional second moments. We derive the asymptotic distribution of the new estimator and show that it does not depend on the estimators of the third and fourth moments. A simulation study shows that the efficiency gains over the GQMLE can be non‐trivial. [ABSTRACT FROM AUTHOR]

This study investigates the influence of pregnancy on the in vivo activity of the intestinal P‐glycoprotein (P‐gp) and hepatic organic anion transporters polypeptide (OATP/BCRP) using, respectively, fexofenadine and rosuvastatin as probe drugs. Eleven healthy participants were investigated during the third trimester of pregnancy (Phase 1, 28 to 38 weeks of gestation) and in the postpartum period (Phase 2, 8 to 12 weeks postpartum). In both phases, after administration of a single oral dose of fexofenadine (60 mg) and rosuvastatin (5 mg), serial blood samples were collected for up to 24 h. Rosuvastatin and fexofenadine in plasma were analyzed by LC‐MS/MS using previously validated methods. The pharmacokinetic parameters of fexofenadine and rosuvastatin (Phoenix WinNonLin software) with normal distribution (Shapiro–Wilk test) are presented as geometric mean and 90% confidence interval. Phases 1 and 2 were compared using the t test (P < .05). Fexofexadine AUC0‐24 values do not differ (P‐value: .0715) between Phase 1 (641.9 ng h/mL [500.6‐823.1]) and Phase 2 (823.8 ng h/mL [641.5‐1057.6]) showing that pregnancy (third trimester) does not alter intestinal P‐gp activity. However, rosuvastatin AUC0‐24 values are higher (P‐value: .00005) in Phase 1 (18.7 ng h/mL [13.3‐26.4]) when compared to Phase 2 (9.5 ng h/mL [6.7‐13.4]), suggesting inhibition of OATP1B1/OATP1B3 transporters. In conclusion, pregnancy assessed during the third trimester does not alter the intestinal P‐gp activity but reduces the activity of hepatic OATP1B1/OATP1B3 transporters. Therefore, adjustments in dosage regimens may be necessary for drugs with low therapeutic index, substrates of the OATP1B1/OATP1B3 transporters, administered during the third trimester of pregnancy. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of Bayesian wavelet estimating the mean vector of multivariate normal distribution under a multivariate normal prior distribution based on linear and nonlinear exponential balanced loss functions. The covariance matrix of multivariate normal distribution is considered known. Bayes estimators of mean vector parameter of multivariate normal distribution are achieved. Then two soft shrinkage wavelet threshold estimators based on Stein’s unbiased risk estimate (SURE) and Bayes estimators are provided. Finally, the performance of the soft shrinkage wavelet estimators was checked through simulation study and Electrical Grid Stability Simulated data set. Simulation and real data results showed the better performance of SURE thresholds based on linear and nonlinear exponential balanced loss functions compared to other classical wavelet methods. Also, they showed better performance for SURE threshold based on nonlinear exponential balanced loss function in multivariate normal distribution with small dimensions. [ABSTRACT FROM AUTHOR]

In this paper, the solutions of an extended form of the Fractional-order Neutron Point Kinetics (FNPK) equation in terms of Caputo-time derivatives of the same order are investigated. Instead of using a Caputo derivative, a distributed-order fractional derivative in the Caputo sense was employed in the term of the FNPK equation which is multiplied by the reactivity. This term plays an important role in the description of neutron kinetics during the start-up, shutdown, and steady-state processes in nuclear reactors. The extended (DFNPK) model was solved using the beta, normal, bimodal and Dirac delta distributions to investigate their effect on the transient state solutions of the neutron density. Regardless of the distribution used, the most significant finding is that a destabilizing effect on the neutron density is induced when the mode (or the instant of application of the Dirac delta) of the distribution tends to one while maintaining the orders of the Caputo-time derivatives constant. What defines the destabilizing effect are large magnitude oscillations, a rapid decay, and an oscillation-free steady state with a monotonic increase that is parallel to but somewhat above the trend determined by the FNPK equation. The extended model is anticipated to be effective for modeling neutron density dispersion in a highly heterogeneous medium that may be described using distributed derivatives. [ABSTRACT FROM AUTHOR]

It is known that different types of music used during sports performance has different psycho-physiological effects. In this context, this study aimed to reveal the effect of different types of music on ITN test performance in tennis players. A total of 35 recreational tennis players voluntarily participated in the study. In the research, the ITN test performance of tennis players was measured in three different conditions with 48-hour intervals, these being without music, with motivational music, and with sedative music. The Freidman test was used in the analysis of the data that did not show a normal distribution, and the Repeated Measures ANOVA test was used in the analysis of the data that showed a normal distribution. According to the main findings of the study, it was determined that motivational music increased the ITN test performance of tennis players, while sedative music decreased their ITN test performance (p<.05). Additionally, it was determined that motivational music increased the groundstroke depth scores of tennis players, while sedative music decreased groundstroke depth scores (p<.05). In addition to this, it was determined that volley depth, groundstroke accuracy, and serve scores increased through motivational music (p<.05), whereas sedative music had no effect (p>.05). As a result, it was determined that the ITN test performances of tennis players can be increased through the psycho-physiological effect of motivational music. It can therefore be concluded that the use of motivational music during training and matches (between sets and/or time breaks) of tennis players can increase their shooting performance. [ABSTRACT FROM AUTHOR]

This study aimed to quantitatively assess the statistical contributions between foreign and national players in men's Euroleague Basketball. Data from 588 games in the 2021–2022 regular season and 612 games in the 2022–2023 regular season were analyzed through non-participant observation. Paired t-tests and Wilcoxon tests were employed to analyse variables with normal and non-normal distributions, respectively. The analysis indicated significant differences (p<0.05) between local and foreign players across several key variables, including Minutes, Points, Average Points, Usage Percentage, Individual Offensive Rating, Individual Defensive Rating, and True Shooting Percentage. These findings suggest pronounced distinctions between foreign players and national players concerning game volume indicators and game performance efficiency. Foreign players exhibited dominance in critical areas, such as playing time, total points scored, and average points per game, underscoring their substantial contributions to their respective teams. Consequently, these results offer practical implications for players, coaches, and fitness trainers, allowing for the design of more tailored training programs that account for distinct offensive and defensive needs, as well as the heightened physical demands experienced throughout the season. [ABSTRACT FROM AUTHOR]

Blood vessels in the retina become damaged as a result of diabetes. If it is not treated early, then it leads to Diabetic retinopathy (DR), which is a significant reason for blindness. Clinical tests are needed to detect and classify the stages, but these are very expensive and time-consuming. This paper proposes an enhanced Gaussian distribution-based image enhancement and segmentation to detect diabetic retinopathy. Medical images have high noise and artefacts, making it difficult to recognize the details with the normal eye and very tough to process the image further. The existing approaches to enhance medical images are very complex and time-consuming. We proposed a more effectiveenhanced Gaussian distribution approach to overcome this limitation. The lesions' inconsistent size and noise in the fundus image make it challenging to segment the lesion. In this study, an improved regularization function in the convolution neural network(CNN) was applied to the retina images to detect the lesions automatically and reduce the overfitting, reducing loss. An improved Support Vector Machine(ISVM) classifies the segmented fundus images. The proposed improved CNN model is compared with the previously carried out studies, and the results prove that the improved CNN model is efficient in diagnosing diabetic retinopathy. [ABSTRACT FROM AUTHOR]

• a de novo missense mutation c.671 T > C (p.F224S) in the GABRB2 gene. • The patient bearing this mutant has epilepsy and developmental delay. • GABA A R bearing mutant β2 subunit showed decreased response to GABA. Genetic variants in genes encoding subunits of the γ-aminobutyric acid-A receptor (GABA A R) have been found to cause neurodevelopmental disorders and epileptic encephalopathy. In a patient with epilepsy and developmental delay, a de novo heterozygous missense mutation c.671 T > C (p.F224S) was discovered in the GABRB2 gene, which encodes the β2 subunit of GABA A R. Based on previous studies on GABRB2 variants, this new GABRB2 variant (F224S) would be pathogenic. To confirm and investigate the effects of this GABRB2 mutation on GABA A R channel function, we conducted transient expression experiments using GABA A R subunits in HEK293T cells. The GABA A Rs containing mutant β2 (F224S) subunit showed poor trafficking to the cell membrane, while the expression and distribution of the normal α1 and γ2 subunits were unaffected. Furthermore, the peak current amplitude of the GABA A R containing the β2 (F224S) subunit was significantly smaller compared to the wild type GABA A R. We propose that GABRB2 variant F224S is pathogenic and GABA A Rs containing this β2 mutant reduce response to GABA under physiological conditions, which could potentially disrupt the excitation/inhibition balance in the brain, leading to epilepsy. [ABSTRACT FROM AUTHOR]

Magnetosonic (MS) waves with frequencies above the proton gyrofrequency can be locally generated by ring‐beam protons in the Martian heavy ion‐rich ionosphere. In this study, we conduct a parametric analysis to investigate the effects of heavy ion concentrations, energy (Erb), and angle (αrb) of ring‐beam protons, and wave normal angle on the excitation features of Martian ionospheric MS waves. We find the growth rates and frequency range of MS waves decrease by including O+ and O2+ ions but are insensitive to their relative concentrations. With increasing Erb or αrb, the growth rates of MS waves show a general dropping tendency. Meanwhile, their frequency and wavenumber range are almost unaffected by increasing Erb but shrink to a narrower range mainly distributed in high frequencies by increasing αrb. Unstable MS waves expand to a wider wavenumber range but shrink to a narrower frequency range as they become more oblique. Plain Language Summary: Magnetosonic (MS) waves are highly compressible electromagnetic emissions in space. Generally, they are locally excited by ring‐like hot protons in plasmas that lack heavy ions. However, a recent study reveals that they can also be locally excited by ring‐beam protons in the Martian heavy ion‐rich ionosphere. Motivated by these differences, we conduct a detailed parametric analysis to investigate how the heavy ion concentrations, the energy and angle of ring‐beam protons, and the wave normal angle affect the dispersion relation and growth rate of Martian MS wave. We find that O+ and O2+ ions lower the growth rates and frequency range of MS waves but the effects of their relative concentrations are insignificant. In addition to the heavy ions, the excitation features of MS waves strongly depend on the wave normal angle and the distribution properties of ring‐beam protons. These results deepen our understanding of the MS wave excitation features in the unmagnetized planet environment with plentiful heavy ions. Key Points: O+ and O2+ ions lower the growth rates and frequency range of Magnetosonic (MS) waves but the effects of their relative concentrations are insignificantThe growth rates of MS waves show a general dropping tendency with increasing ring‐beam energy or angleUnstable MS waves expand to a wider wavenumber range but shrink to a narrower frequency range as they become more oblique [ABSTRACT FROM AUTHOR]

Background: In this study, we comprehensively profiled the T‐cell receptor (TCR) repertoire of the tumor and adjacent normal tissue in patients with HBV‐associated hepatocellular carcinoma (HCC) and determined the baseline characteristics and clinical significance of TCR. Methods: High‐throughput sequencing was used to determine the profile of complementarity‐determining region 3 (CDR3) of the TCR‐β chain variable (TRBV) in the tumor and normal tissue samples of 14 HCC patients. At the same time, TRBV diversity and differences in expression between tumor and normal tissues were investigated. The cumulative frequency of top 100 CDR3 (CF100), clonality, and Shannon entropy as indices to evaluate diversity, Results: The diversity of TRBV CDR3 showed no significant difference between tumor and normal tissues. Of the 58 V gene segments in TRBV, TRBV16 and TRBV7‐6 had a significantly higher frequency in the tumor group than in the normal group (p < 0.05). The frequency of 14 J gene segments showed no significant difference between tumor and normal tissues. In contrast, the frequency of 22 TRBVx/BJx combinations was significantly higher in the tumor than in the normal tissue. In addition, the length and type of TRBV CDR3 were similar in tumor and normal tissues, and a Gaussian distribution was observed in both groups. Conclusion: This study provided a large amount of information about the TCR lineage in HBV‐associated HCC, laying the foundation for further research. In addition, the fact that the immune repertoire (TRBV CDR3) hardly differs between tumor and adjacent normal tissue provides a new clue for exploring the mechanism of the liver as an organ with immune privileges. [ABSTRACT FROM AUTHOR]

Galaxy cluster masses derived from observations of weak lensing suffer from a number of biases affecting the accuracy of mass-observable relations calibrated from such observations. In particular, the choice of the cluster centre plays a prominent role in biasing inferred masses. In the past, empirical miscentring distributions have been used to address this issue. Using hydrodynamic simulations, we aim to test the accuracy of weak lensing mass bias predictions based on such miscentring distributions by comparing the results to mass biases computed directly using intracluster medium (ICM)-based centres from the same simulation. We construct models for fitting masses to both centred and miscentred Navarro–Frenk–White profiles of reduced shear, and model the resulting distributions of mass bias with normal and lognormal distributions. We find that the standard approach of using miscentring distributions leads to an overestimation of cluster masses at levels of between 2 per cent and 6 per cent when compared to the analysis in which actual simulated ICM centres are used, even when the underlying miscentring distributions match in terms of the miscentring amplitude. While we find that neither lognormal nor normal distributions are generally reliable for accurately modelling the shapes of the mass bias distributions, both models can serve as reasonable approximations in practice. [ABSTRACT FROM AUTHOR]

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels, α = 0.05 and α = 0.01 , we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Cramér–von Mises (CVM), Lilliefors (LF), and Shapiro–Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes n = 25 , 50 , 75 , 100 , 150 , 200 , 250 , 500 , and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "On-Farm Methane Mitigation and Animal Health Assessment of a Commercially Available Tannin Supplement in Organic Dairy Heifers." The correction addresses an error in the methodology for determining average daily gain in the original publication. The correction also includes updated tables with corrected means and variances for methane emissions and average daily gain. The authors state that the scientific conclusions of the study are unaffected by these corrections. The study examined the effects of different levels of tannin supplementation on parameters such as average daily gain, final body weight, dry matter intake, total mixed ration, sweet feed, GreenFeed bait pellets, and feed efficiency. The results showed that tannin supplementation did not significantly affect most of these parameters, but there were some differences observed in average daily gain and final body weight between the control group and the groups with different levels of tannin supplementation. Further research is needed to fully understand the impact of tannin supplementation on heifer performance. [Extracted from the article]

Nonlocal models have demonstrated their indispensability in numerical simulations across a spectrum of critical domains, ranging from analyzing crack and fracture behavior in structural engineering to modeling anomalous diffusion phenomena in materials science and simulating convection processes in heterogeneous environments. In this study, we present a novel framework for constructing nonlocal convection–diffusion models using Gaussian‐type kernels. Our framework uniquely formulates the diffusion term by correlating the constant diffusion coefficient with the variance of the Gaussian kernel. Simultaneously, the convection term is defined by integrating the variable velocity field into the kernel as the expectation of a multivariate Gaussian distribution, facilitating a comprehensive representation of convective transport phenomena. We rigorously establish the well‐posedness of the proposed nonlocal model and derive a maximum principle to ensure its stability and reliability in numerical simulations. Furthermore, we develop a meshfree discretization scheme tailored for numerically simulating our model, designed to uphold both the discrete maximum principle and asymptotic compatibility. Through extensive numerical experiments, we validate the efficacy and versatility of our framework, demonstrating its superior performance compared to existing approaches. [ABSTRACT FROM AUTHOR]

Background Objective Methods Results Conclusion The prevalence and impact of obesity on outcomes of atrial fibrillation (AF) ablation randomized controlled trials (RCTs) have not been well studied.To examine the proportion of participants with obesity enrolled in RCTs of AF ablation and outcomes of ablation when subgroup analysis of participants with obesity were available.We systematically searched PubMed and EMBASE for AF ablation RCTs published between January 1, 2015 to May 31, 2022. When body mass index (BMI) data were available, normal distribution was assumed and a z score was used to estimate the proportion of obesity. Results categorized by BMI or body weight status were reviewed. Authors were contacted for additional information.Of 148 eligible RCTs with 30174 participants, 144 (97.30%) RCTs did not report the proportion of participants with obesity, while published information regarding BMI was available in 63.51%. Three trials excluded patients based on BMI. Using reported BMI, we estimated the proportion of participants with obesity varied greatly across these trials, ranging from 5.82%–71.9% (median 38.02%, interquartile 29.64%, 49.10%). Patients with obesity were represented in a greater proportion among trials conducted in North America (50.23%) and Asia (44.72%), compared to others (32.16%), p < .001. Subgroup analysis or analysis adjusting for BMI was reported in only 13 (8.78%) RCTs; four (30.77%) of these suggested that BMI or body weight might negatively affect primary outcomes.Obesity is a common comorbidity among AF patients. However, most AF ablation RCTs underreported the proportion of participants with obesity and its impact on the primary outcomes. [ABSTRACT FROM AUTHOR]

Summary The mixture models are widely used to analyze data with cluster structures and the mixture of Gaussians is most common in practical applications. The use of mixtures involving other multivariate distributions, like the multivariate skew normal and multivariate generalised hyperbolic, is also found in the literature. However, in all such cases, only the mixtures of identical distributions are used to form a mixture model. We present an innovative and versatile approach for constructing mixture models involving identical and non‐identical distributions combined in all conceivable permutations (e.g. a mixture of multivariate skew normal and multivariate generalised hyperbolic). We also establish any conventional mixture model as a distinctive particular case of our proposed framework. The practical efficacy of our model is shown through its application to both simulated and real‐world data sets. Our comprehensive and flexible model excels at recognising inherent patterns and accurately estimating parameters. [ABSTRACT FROM AUTHOR]